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Local Lipschitz Continuity in the Initial Value and Strong Completeness for Nonlinear Stochastic Differential Equations
16 references·3 citing·28 second hop
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References

  • 1999Continuous Martingales and Brownian Motion6,200 cited
  • 2007A Concise Course on Stochastic Partial Differential Equations803 cited
  • 2012Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients428 cited
  • 1996Existence of strong solutions for Itô's stochastic equations via approximations400 cited
  • 1977A comparison theorem for solutions of stochastic differential equations and its applications304 cited
  • 2005On the discretization schemes for the CIR (and Bessel squared) processes246 cited
  • 2014Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients227 cited
  • 2013A note on tamed Euler approximations185 cited
  • 2016Euler approximations with varying coefficients: The case of superlinearly growing diffusion coefficients174 cited
  • 2011An Euler-type method for the strong approximation of the Cox–Ingersoll–Ross process147 cited
  • 2014First order strong approximations of scalar SDEs defined in a domain134 cited
  • 2020On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients128 cited
  • 2012Strong convergence rates for backward Euler–Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients113 cited

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  • 2015Loss of regularity for Kolmogorov equations81 cited
  • 2002An Interest Rate Model with Upper and Lower Bounds77 cited
  • 1981On the strong comparison theorems for solutions of stochastic differential equations64 cited
  • Cited by

    • 2020Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks52 cited
    • 2016Rough differential equations with unbounded drift term37 cited
    • 2014Strong convergence rates and temporal regularity for Cox-Ingersoll-Ross processes and Bessel processes with accessible boundaries27 cited